Since you know the anti derivative, let's call it F, is F(x) = arctan e^x + C,
you simply need to evaluate F(1) - F(0)
but because you are subtracting the two functions, you don't have to work with the C, because C - C = 0
So it's arctan(e^1) - arctan(e^0) = arctan(e) - arctan(1)